The Sitnikov problem is a restricted three body problem where the
eccentricity of the primaries acts as a parameter. We find
families of symmetric periodic solutions bifurcating from the
equilibrium at the center of mass. These families admit a global continuation up to excentricity $e=1$. The same techniques are applicable to the families obtained by continuation from the circular problem ($e=0$). They lead to a refinement of a result obtained by J. Llibre and R. Ortega.